Frobenius bimodules are connected with Frobenius algebras and extensions. For instance, a ring extension φ : R → S is a Frobenius extension if and only if RSS is a Frobenius bimodule [1]. Brzeziński and Gómez-Torrecillas studied in [4] certain properties of comatrix corings in relation to properties of bimodules. In particular they showed that the comatrix coring [6] induced by any Frobenius bi...

Suppose S is an affine, noetherian scheme, X is a separated, noetherian S-scheme, E is a coherent OX -bimodule and I ⊂ T (E) is a graded ideal. We study the geometry of the functor Γn of flat families of truncated B = T (E)/I-point modules of length n + 1. We then use the results of our study to show that the point modules over B are parameterized by the closed points of P X2(E). When X = P , w...

Abstract We study higher-form global symmetries and a higher-group structure of low-energy limit (3 + 1)-dimensional axion electrodynamics in gapped phase described by topological action. argue that the should have semi-strict 4-group (3-crossed module) consistency conditions couplings action to background gauge fields for symmetries. find possible ’t Hooft anomalies symmetry, discuss physical ...

We present a new compositional approach to game theory (CGT) based upon Arrows, concept originally from functional programming, closely related Tambara modules, and operators build Arrows old. model equilibria as bimodule over an Arrow define operator such existing Arrow. also strategies graded which builds by taking the colimit of A final bimodule. use this CGT show how known previously unknow...

We introduce the concept of reflexivity for bounded n-linear maps and investigate the reflexivity of Zn(L1(G),X), the space of bounded ncocycles from L1(G)(n) into X, where L1(G) is the group algebra of a locally compact group G and X is a Banach L1(G)-bimodule. We show that Zn(L1(G), X) is reflexive for a large class of groups including groups with polynomial growth, IN-groups, maximally almos...

Applying geometric methods of 2-dimensional cell complex theory, we construct a Galois covering bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects finite representation type. Each admitted A is endowed with quasi multiplicative basis. The main result shows that for from considered class having restrictions schurian universal A', ...

Definition 3. Let B be a ring. Then, we denote by B [[t]] the ring of formal power series over B in the indeterminate t, where t is supposed to commute with every element of B. Formally, this means that we define B [[t]] as the ring of all sequences (b0, b1, b2, ...) ∈ BN (where N means the set {0, 1, 2, ...}), with addition defined by (b0, b1, b2, ...) + (b ′ 0, b ′ 1, b ′ 2, ...) = (b0 + b ′ ...

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...